Edexcel Core Mathematics C4 June 2011
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Edexcel Core Mathematics C4 June 2011 Past Paper
C4 Mathematics Edexcel June 2011 Question 6
6. With respect to a fixed origin O, the lines l1
are given by the equations.
where λ and μ are scalar parameters.
(a) Show that ll and l2 meet and find the position vector of their point of intersection A.
(b) Find, to the nearest 0.1°, the acute angle between l1 and l2
The point B has position vector
(c) Show that B lies on l1
(d) Find the shortest distance from B to the line l2, giving your answer to 3 significant figures.
6 (a) Vectors
6 (b) Vectors
C4 Mathematics Edexcel June 2011 Question 7
Figure 3 shows part of the curve C with parametric equations
x = tanθ, y = sinθ
, 0 ≤ θ < π/2
The point P lies on C and has coordinates (√3, ½√3)
(a) Find the value of ș at the point P.
The line l is a normal to C at P. The normal cuts the x-axis at the point Q.
(b) Show that Q has coordinates (k√3, 0) , giving the value of the constant k.
The finite shaded region S shown in Figure 3 is bounded by the curve C, the line x = √3 and the x-axis. This shaded region is rotated through 2π radians about the x-axis to form a solid of revolution.
(c) Find the volume of the solid of revolution, giving your answer in the form pπ√3 + qπ2, where p and q are constants.
7 (a) Parametric equations
7 (b) Normal to a Parametric Curve
7 (c) Volume of Revolution to a Parametric Curve
C4 Mathematics Edexcel June 2011 Question 8
8. (a) Find ∫(4y + 3)-1/2
(b) Given that y =1.5 at x = – 2, solve the differential equation
dy/dx = √(4y + 3)/x2
giving your answer in the form y x = f( ).
8 (a) Integration methods
8 (b) Differential Equations
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